MambaH-Fit: Rethinking Hyper-surface Fitting-based Point Cloud Normal Estimation via State Space Modelling

TL;DR

MambaH-Fit presents a state-space modelling framework for point cloud normal estimation that emphasizes fine-grained local geometry. By coupling an Attention-driven Hierarchical Feature Fusion (AHFF) module with a Patch-wise State Space Model (PSSM), the approach enables adaptive multi-scale context learning and implicit hyper-surface fitting within local patches using Mamba blocks. Extensive experiments across synthetic and real-world datasets demonstrate improved accuracy, robustness, and generalization over existing methods, with ablations validating the contributions of AHFF and PSSM. The work demonstrates practical impact in downstream tasks such as surface reconstruction and point cloud filtering, highlighting the method’s scalability to large-scale real-world scans.

Abstract

We present MambaH-Fit, a state space modelling framework tailored for hyper-surface fitting-based point cloud normal estimation. Existing normal estimation methods often fall short in modelling fine-grained geometric structures, thereby limiting the accuracy of the predicted normals. Recently, state space models (SSMs), particularly Mamba, have demonstrated strong modelling capability by capturing long-range dependencies with linear complexity and inspired adaptations to point cloud processing. However, existing Mamba-based approaches primarily focus on understanding global shape structures, leaving the modelling of local, fine-grained geometric details largely under-explored. To address the issues above, we first introduce an Attention-driven Hierarchical Feature Fusion (AHFF) scheme to adaptively fuse multi-scale point cloud patch features, significantly enhancing geometric context learning in local point cloud neighbourhoods. Building upon this, we further propose Patch-wise State Space Model (PSSM) that models point cloud patches as implicit hyper-surfaces via state dynamics, enabling effective fine-grained geometric understanding for normal prediction. Extensive experiments on benchmark datasets show that our method outperforms existing ones in terms of accuracy, robustness, and flexibility. Ablation studies further validate the contribution of the proposed components.

Figures (12)

• Figure 1: Left: Normal estimation results from different surface fitting methods, with comparisons to the ground-truth normal direction and point-wise weights visualised. Right: The bottom values indicate RMSE for normal prediction, where our method achieves more accurate results. The angular error is listed in degrees.
• Figure 2: Overview of MambaH-Fit's architecture. Our AHFF module enables adaptive hierarchical feature fusion for $G$. $C_G$ and $C_C$ represent encoding dimensions for feature codes $G$ and $C$, respectively. In our PSSM module, point features $\{\mathbf{x}_1, \ldots, \mathbf{x}_M\}$ (as tokens) are naturally ordered by each point's spatial distance to the patch's query point.
• Figure 3: Illustration of our AHFF module's attention-driven fusion scheme. We visualise the attention weights on the $N_s$-point patch, where geometric features (e.g., fluctuating regions), which are not necessarily near the patch centre, are assigned higher weights.
• Figure 4: Demonstration of Mamba's effectiveness on diverse surface geometries. We visualise the predicted normal's accuracy, point-wise weight $w_i$, and each patch's corresponding mesh surface.
• Figure 5: PGP$\alpha$ on different PCPNet test settings.